2015 Classes

Here is an overview of our courses from this summer. You can read the class descriptions ("blurbs"), view the global schedule in a grid, or see all the classes sorted by category.

Read the 2015 Blurbs

View the 2015 Schedule

Here is the list of classes by subject:

Algebra

• A (re)Introduction to Polynomials
• A Dynkin diagram miscellany
• Abel's Theorem
• Abelian Groups
• Abstract Nonsense
• Advanced Linear Algebra
• Braid Groups
• Burnside's Lemma
• Category Theory in Sets
• Cyclotomic Polynomials and Extensions
• Extensions
• Finite Fields
• Galois Theory
• Introduction to Groups
• Laurent Phenomenon
• Lie Algebras
• Linear Algebra
• Primitive roots
• Reflection Groups
• Representation Theory of Finite Groups
• Ring Theory
• Sylow Theorems
• The Banach–Tarski Paradox
• The tale of summation is in order!
• Tiling Problems
• Tropical Curves
• Colloquium: Putting the Algebra in Algebraic Topology

Analysis

• Almost All You Want
• Differentials and higher differentials
• Differentiation under the Integral Sign
• Functions of a Complex Variable
• Fundamental Theorem of Calculus in Dimension n
• Infinitesimals
• Lebesgue Measure
• Metric Spaces
• Multivariable Calculus
• Normal Numbers
• The Ham Sandwich Theorem and Friends
• What's Up With e?
• Colloquium: Cauchy's functional equation

Applied Math

• A Card Trick, and a Set
• A Mathematician Goes to Vegas
• Building a machine that learns like a human
• Cosine Waves on Musical Staves
• From Geometric Optics to High Speed Underwater Photography
• Group operations' harmonic implications
• Mathematical Magic
• Optimization Problems on Graphs
• Quantum factoring
• Special Relativity
• Statistical Modelling
• The Cake is a Lie
• The Fast More Four Do Over
• The Hidden Dance of Partial Differential Equations
• The mathematics of polygamy (and bankruptcy)
• Time-Frequency Analysis
• Unsolved Problems in Cosmology
• Voting Theory
• Colloquium: An Intro to "Data Science"
• Colloquium: Pad Thai with Electrons
• Colloquium: Secure Genomic Computation: a Contest

Combinatorics

• Coloring Maps
• Combinatorial Game Theory
• From Counting to a Theorem of Fermat
• Generating Functions, Catalan Numbers, and Partitions
• Graphs on Surfaces
• Induced Matchings from Szemeredi's Regularity Lemma
• Intro Knot Theory
• Knight's Tours
• Latin Squares
• Posets
• Qualifying Quiz Problem 6
• Summing Series
• The Hoffmann Singleton Theorem
• The Pruefer Correspondence
• The Robinson-Schensted Correspondence
• The Tower of Hanoi
• Tower of Hanoi
• Unlikely Maths
• Wagner's Theorem
• Colloquium: Triples

Computer Science

• Algorithms
• Automated Proofs in Geometry
• Cryptography
• Cryptography: What is it and Why Do we Care?
• Error-Correcting Codes
• Introduction to Complexity
• Learn to code!
• Many Facets of Optimization
• P vs NP
• Colloquium: Computers: Friends or foes of the modern mathematician?

Geometry

• Aperiodic Tiling
• Apollonian Circle Packings
• Classifying Symmetry
• Coloring in Space
• Counting the Faces of Cut-Up Spaces
• DIY Hyperbolic Geometry
• Elliptic Curves Day 1
• Fractal dimensions
• Non-classical Constructions
• Quaternions and rotations
• Quaternions and rotations
• Shortest Distance
• The Projective Plane
• Colloquium: Can You Hear the Shape of a Drum?
• Colloquium: Neural Codes
• Colloquium: Polyhedral Symmetry in the Plane?

History, Literature, and Education

• Bad History: A Crash Course in Historiography and how not to do the History of Math
• Development of Probability
• History of Math
• The History of Calculus
• Turing and his Work
• Colloquium: Are We Special?
• Colloquium: Finding my Place in {Teacher Educators} ∩ {Mathematicians}: Bringing a Mathematical Eye to Teacher Education

Logic/Set Theory

• A game you can't play (but would win if you could)
• Exploring Equality via Homotopy and Proof Assistants
• Fun with Compactness in Logic
• LARGE cardinals!
• Martin's Axiom and Ramsey Ultrafilters
• Mathcamp Crash Course
• Measure and Martin's Axiom
• Ordinal Arithmetic
• Stupid Games on Uncountable Sets
• The Löwenheim-Skolem Theorem
• Ultrafilters
• Colloquium: Hydras
• Colloquium: Making Cantor Super Proud

Number Theory

• Absolute Values: All the Other Ones
• Algorithms in Number Theory
• Continued Fractions
• Multiplicative Functions
• Quadratic Reciprocity
• The Factorial Function
• pNumber Theory
• Colloquium: My Favorite Prime

Probability/Statistics

• Markov Chains to Support your Probabilistic Exploits

Problem Solving

• Problem Solving: Combinatorics
• Problem Solving: Inequalities
• Problem Solving: Linear Algebra
• Problem Solving: Tetrahedra
• Rapid Fire Problem Solving

Topology

• Classifying Spaces
• Combinatorial Topology
• Fundamental Group
• Galois Cohomology
• Homotopy Theory
• Point-set Topology
• Colloquium: Reeb Foliation of the 3-Sphere